Proof From [1]}, we know that:
\(\max _{z \in \mathcal {Z}_{\mathcal {D}}}|\mathbf {{\color {red}s}}_{{{\color {red}\mathbf {P}}}}(\mathbf {z}) - {\color {c2}\tilde{\mathbf {s}}}_{{\color {c2}\tilde{\mathbf {P}}}}(\mathbf {z})| \le \sup _{x \in \mathcal {X}}||\mathbf {{\color {red}s}}_{{{\color {red}\mathbf {P}}}}(\mathbf {x}) - {\color {c2}\tilde{\mathbf {s}}}_{{\color {c2}\tilde{\mathbf {P}}}}(\mathbf {x})||\le R_{\mathcal {X}}\cdot \beta \cdot \left(1+\nu + \frac{\beta }{N_L}\right)^{N_L} \cdot d_{NN}({{\color {red}\mathbf {P}}}, {\color {c2}\tilde{\mathbf {P}}}).\) 
